Method and apparatus for determining gate capacitance

ABSTRACT

Provided is a method of determining a gate capacitance of a semiconductor device having a source, a drain, a gate, and a channel, the semiconductor device being arranged in a circuit further comprising an electrical resonator, wherein one of the source, the drain, and the gate is connected to the electrical resonator. The method comprises: measuring a resonance frequency of the circuit; and calculating, based on the resonance frequency, the gate capacitance. Since it is not necessary to pass a current through the semiconductor device, an accurate measurement of gate capacitance may be achieved. Also provided are an apparatus for determining a gate capacitance, a probe for measuring gate capacitance, and a related computer program product.

BACKGROUND

Various types of semiconductor devices include a gate. A gate is anelectrode which is configured to apply an electrostatic field to aportion of semiconductor material, which portion may be referred to as achannel. The electrostatic field may vary the number of available chargecarriers in the semiconductor material, thereby allowing control overthe electrical properties of the semiconductor material.

It is typically desirable to minimise any flow of current between thegate to the semiconductor material. Any such current is referred to asleakage current. To this end, the gate is separated from thesemiconductor material by a dielectric. The dielectric may include anair gap, or a layer of material.

Charge in the gate is separated from charge in the semiconductormaterial by the dielectric. This means that the gate structure has acapacitance, which is referred to as a gate capacitance. Measurements ofgate capacitance may provide useful information about the electronicbehaviour of the device, the properties of the semiconductor material,the properties of the dielectric material, etc.

An existing method for determining gate capacitance is referred to asthe capacitance-voltage, or C-V, method. This method involves applyingAC currents directly to the semiconductor component. A limitation ofthis method is that the signal obtained can be noisy.

One class of semiconductor device which is of particular researchinterest is semiconductor-superconductor hybrid devices. These devicesare useful for quantum computing. In a hybrid device, energy levelhybridisation, also referred to as coupling, between a semiconductor anda superconductor may occur under certain conditions. Excitations whichare useful for quantum computing, for example Majorana zero modes, maybe induced in such a device. Inducing such excitations may involveapplying a magnetic field to the device, as well as electrostaticallygating one or more portions of the device. The structure and fabricationof one example hybrid device are disclosed in WO 2019/001753 A1.

SUMMARY

One aspect provides a method of determining a gate capacitance of asemiconductor device having a source, a drain, a gate, and a channel,the semiconductor device being arranged in a circuit further comprisingan electrical resonator, wherein one of the source, the gate, and thedrain is connected to the electrical resonator; the method comprising:measuring a resonance frequency of the circuit; and calculating, basedon the resonance frequency, the gate capacitance.

Another aspect provides an apparatus for determining a gate capacitanceof a semiconductor device, the semiconductor device having a having asource, a drain, a gate, and a channel; the apparatus comprising: asignal generator capable of providing a probe signal to an electricalresonator; a sensor capable of sensing at least one of the amplitude andthe phase of a response signal from the electrical resonator; aprocessing unit operably linked to the signal generator and the sensor;and a memory unit operably linked to the processing unit, wherein thememory unit stores computer program code, the computer program codebeing executable by the processing unit; wherein the computer programcode comprises: a control module for causing the processing unit tocontrol the signal generator; an identification module for causing theprocessing unit to identify, based on an input from the sensor, aresonance frequency of a circuit comprising the electrical resonator; acalculation module for causing the processing unit to calculate, basedon the resonance frequency, the gate capacitance of the semiconductordevice; and an output generation module for generating an outputidentifying the gate capacitance.

A still further aspect provides a probe for measuring gate capacitance,comprising a needle probe, an inductor, and a capacitor; wherein theneedle probe, inductor and capacitor are configured as an LC circuit;and wherein the probe is configured to be connectable to an apparatus toreceive a probe signal from the apparatus and to provide a responsesignal from the LC circuit to the apparatus.

Another aspect provides a computer program product embodied on anon-transitory computer readable medium, comprising computer programcode which, when executed by a processor, causes the processor to:process an input to identify a resonance frequency of a circuitcomprising an electrical resonator; calculate, based on the resonancefrequency, a gate capacitance; and generate an output identifying thegate capacitance.

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used to limit the scope of the claimed subject matter. Nor is theclaimed subject matter limited to implementations that solve any or allof the disadvantages noted herein.

BRIEF DESCRIPTION OF THE DRAWINGS

To assist understanding of embodiments of the present disclosure and toshow how such embodiments may be put into effect, reference is made, byway of example only, to the accompanying drawings in which:

FIG. 1 is a diagram of a first example of a circuit for measuring gatecapacitance, the circuit including an LC resonator;

FIG. 2 is a flow chart outlining a method of measuring gate capacitance;

FIG. 3 is a diagram of a second example of a circuit for measuring gatecapacitance, the circuit including a transmission line resonator;

FIG. 4 is a schematic diagram of an apparatus for measuring gatecapacitance;

FIG. 5 is a schematic diagram of a probe of the present disclosure;

FIG. 6 is an annotated scanning electron microscopy, SEM, micrograph ofa semiconductor-superconductor hybrid device having a plurality offinger gates, investigated in Example 1;

FIG. 7 is a plot showing: (a) the resonance frequency of the resonatorused in Example 1 (• symbols, left-hand axis), and (b) calculatedadditional gate capacitance of the FIG. 6 device (+ symbols, right-handaxis), each as a function of the number of active finger gates;

FIG. 8 is a diagram of a circuit which was simulated in Example 2;

FIG. 9 is a plot comparing gate capacitance calculated from a resonancefrequency against the input gate capacitance in the simulations ofExample 2; and

FIG. 10 is a plot of relative error against input gate capacitance,derived from the data of FIG. 9 .

DETAILED DESCRIPTION OF EMBODIMENTS

As used herein, the verb ‘to comprise’ is used as shorthand for ‘toinclude or to consist of’. In other words, although the verb ‘tocomprise’ is intended to be an open term, the replacement of this termwith the closed term ‘to consist of’ is explicitly contemplated.

In the context of the present disclosure, a signal is an electricalsignal having a frequency, a phase, and an amplitude.

Described herein is a method of determining a gate capacitance of asemiconductor device, such as a semiconductor-superconductor hybriddevice. The method makes use of an electrical resonator. The resonatoris connected to the device under investigation. This causes a change inthe resonance frequency of the resonator. The gate capacitance of thedevice may be calculated from the resonance frequency of thedevice-resonator system. The method may, for example, allow measurementsof gate capacitance with a better signal-to-noise ratio than existingmethods.

The principles of the method will now be explained with reference toFIGS. 1 and 2 . FIG. 1 is a diagram of an example circuit useful forpractising the method, and FIG. 2 is a flowchart outlining the method.

The illustrated circuit 100 allows for measurement of the resonancefrequency of a system made up of an electrical resonator unit 120 and asemiconductor device 140. Semiconductor device 140 in this example is atransistor. A transistor has a source terminal which is connected to adrain terminal by a portion of semiconductor material. The portion ofsemiconductor material is referred to as a channel. The transistorfurther includes a gate electrode for applying an electrostatic field tothe channel in order to modify the number of available charge carriersin the channel.

Although the illustrated example shows a transistor, the method providedherein may be applied to any type of semiconductor device which includesa source, a drain, a channel, and a gate. For example, asemiconductor-superconductor hybrid device may include a semiconductorcomponent in the form of a nanowire; an electrical contact at each endof the nanowire; one or more gate electrodes for applying anelectrostatic field to one or more portions of the nanowire; and asuperconductor component configured to be capable of undergoing energylevel hybridisation with the semiconductor. In such a structure, theelectrical contacts represent a source and a drain, and the one or moreportions of the nanowire represent a channel.

Semiconductor device 140 is depicted as an N-type MOSFET. This is oneillustrative example of a semiconductor device in which the density ofcharge carriers in the channel can be varied by applying a gate voltage.Any other gated semiconductor device may be investigated using thepresent methods.

The source of semiconductor device 140 is connected to one end of anelectrical resonator unit 120 via a low impedance contact 130. The drainof semiconductor device 140 is connected to a high impedance contact140. The gate of semiconductor device 140 is connected to a voltagesource 145 for applying an electrostatic field to the gate electrode.

In this example, electrical resonator unit 120 is an LC circuit. An LCcircuit comprises an inductor 122, coupled to a capacitance, representedby capacitor component 124. An LC circuit is one example of anelectrical resonator.

Although FIG. 1 shows a capacitor component 124, the capacitance may beparasitic. Parasitic capacitance, also referred to as stray capacitance,is a capacitance that unavoidably arises from the physical proximity ofcomponents of a circuit.

In most implementations, an LC circuit includes an inductor componentsuch as a coil. Although any conductor through which a current flowswill give rise to a parasitic inductance, in practice parasiticinductances are usually very small.

In implementations when an LC circuit is used, the LC circuit may have anatural resonance frequency in the range 10 MHz to 2 GHz, optionally 30MHz to 1.5 GHz. By “natural resonance frequency” is meant the frequencyof the LC circuit alone, when not connected to a gate capacitance. Aswill be explained in more detail below, the resonance frequency of an LCcircuit may be varied by selecting the magnitudes of the inductance andthe capacitance.

For example, the inductor may have an inductance in the range 100 nH to5 µH. The capacitance may have a magnitude in the range 0.1 pF to 5 pF.One example implementation, which provides a resonance frequency ofapproximately 1.5 GHz, uses an inductance of 100 nH and a capacitance of0.1 pF. Another example implementation, which provides a resonancefrequency of approximately 30 MHz, uses an inductance of 5 µH and acapacitance of 5 pF.

In implementations where the capacitance is a parasitic capacitance, themagnitude of the inductance may be selected to provide a desiredresonance frequency.

The properties of the electrical resonator may be selected to optimizethe sensitivity of the measurement. For example, the impedance of theelectrical resonator may be matched with the impedance of a transmissionline between the IO unit and the electrical resonator may allow forimproved sensitivity. Another possibility is to select the qualityfactor of the resonant circuit based on the resistivity of thesemiconductor device.

In implementations where a capacitor component is present, the capacitormay be a varactor. The capacitance of a varactor may be varied byapplying an electrostatic field to the varactor. Varying the capacitancevaries the natural resonance frequency of the LC circuit. A resonatorwhich has a variable resonance frequency is referred to as tuneable.

Alternatively, a tuneable LC circuit may in principle be implementedusing a variable inductor and a fixed capacitance. A still furtherpossible implementation comprises a variable inductor and a variablecapacitor.

The connection between the electrical resonator unit 120 and the sourceof semiconductor device 140 is a low impedance contact 130. In FIG. 1 ,the low impedance contact 130 is illustrated by resistor 132 andcapacitor 134. Any connector or transmission line will have an intrinsicimpedance, and resistor 132 and capacitor 134 represent this intrinsicimpedance. The impedance of low impedance contact 130 is desirably aslow as possible. The low impedance contact typically does not comprise aresistor component or a capacitor component.

High impedance contact 150, which is connected to the drain of thesemiconductor device 140, is illustrated by a resistor 152 and capacitor154. It is desirable for current flow through the semiconductor devicefrom the source to the drain to be as low as possible, ideally 0. It isalso desirable for any capacitance at the drain contact to be minimised.

The high impedance contact is selected to have an impedance which islarge compared to the impedance of the gate capacitance. The highimpedance contact 150 may comprise a tunnel junction. Alternatively, thehigh impedance contact 150 may comprise a resistor, for example aresistor having a resistance of at least 2 MΩ, optionally at least 10MΩ. Capacitor 154 represents a parasitic capacitance. The parasiticcapacitance of the high impedance contact is desirably as low aspossible.

Alternatively, the drain of the semiconductor device 140 may beconnected to a transistor, for example a field effect transistor. In an“off” state, the transistor may behave as a high impedance contact toallow for measurement of gate capacitance. In an “on” state, thetransistor may allow current to flow from the source to the drain of thesemiconductor device 140, allowing for measurement of conductance of thechannel of the semiconductor device.

Electrical resonator unit 120 and semiconductor device 140 may beconnected permanently. For example, the electrical resonator unit andthe semiconductor device may be fabricated on the same chip or may besoldered into the same circuit. Alternatively, the electrical resonatorunit and semiconductor device 140 may be removably connected. Electricalresonator unit 120 may be implemented as a needle probe, temporarilytouched on a terminal of the semiconductor device, as explained in moredetail below with reference to FIG. 5 . The terminal may be one of thesource, the gate, and the drain.

The circuit 100 further comprises an input-output, IO, unit 110. IO unit110 is connected to the electrical resonator unit 120. IO unit 110 isconfigured to send a probe signal, in the form of an AC current having afrequency and a phase, to the electrical resonator unit 120. The probesignal generated by the IO unit may have a frequency in the range 10 MHzto 10 GHz, for example.

The IO unit 110 may be configured to allow the frequency of the probesignal to be varied. This may allow the input frequency to be scanned tofacilitate detection of the resonance frequency of the electricalresonator unit 120.

In implementations where the circuit includes a tuneable electricalresonator unit, an IO unit 110 which provides a probe signal having afixed frequency may be used. In such implementations, the tuning of theelectrical resonator unit may be varied to obtain resonance, and Cgatemay be inferred based on the variation of the tuning.

In implementations where the phase of the response signal relative tothe probe signal is measured, the IO unit 110 may provide a probe signalhaving a fixed frequency.

IO unit 110 is further configured to detect a response signal from theelectrical resonator unit 120. More specifically, the IO unit 110 isconfigured to detect the amplitude of the response signal and/or phaseof the response signal. In particular, the IO unit may be configured todetect a phase difference between the response signal and the responsesignal. An example of a detector useful for detecting the responsesignal is a vector network analyser. Vector network analysers arecommercially available, one example being the R&S® ZNB Vector NetworkAnalyzer commercialized by Rohde & Schwarz. A vector network analysermay detect both phase and amplitude. Measuring both phase and amplitudemay allow for more accurate determination of the resonance frequency.

In the example circuit, electrical resonator unit 120 is connected tothe source of the semiconductor device 140. The electrical resonatorunit 120 may alternatively be connected to either the drain or the gateof the semiconductor device 140. In other words, the electricalresonator unit connects to the IO unit and any one of the source, thedrain, and the gate.

In variants where the electrical resonator unit 120 is connected to thedrain, the source may be connected to the high impedance contact.

In variants where the electrical resonator unit 120 is connected to thegate, a gate voltage may be applied via the resonator or via a furthergate. Semiconductor devices are typically configured to prevent flow ofcurrent from the gate electrode to the source and drain, e.g., with agate dielectric between the gate and the channel. In other words, thedirect connection between the gate and the source and drain is usuallyhighly resistive. The gate dielectric may act as the high impedancecontact.

The operation of circuit 100 will now be described with reference toFIG. 2 .

At block 201, the resonance frequency of the electrical resonator ismeasured. Various approaches to the measurement of resonance frequencyare possible.

When the frequency of the probe signal generated by the IO unit 110 isclose to the resonance frequency of electrical resonator unit 120, theamplitude and phase of the response signal received from the electricalresonator unit 120 change. The change in amplitude of the responsesignal and/or the change in phase of the response signal are detected bythe IO unit 110.

The resonance frequency may be identified by monitoring the responsesignal received by the IO unit 110 whilst varying the frequency of theprobe signal generated by the IO unit. Alternatively or additionally, inimplementations where the electrical resonator unit 120 is tuneable, thetuning of the electrical resonator unit may be varied. Measurementswhich include varying frequency of the probe signal and/or the tuning ofthe electrical resonator unit may allow for accurate determination ofthe resonance frequency.

Another approach to measuring resonance frequency is to measure adifference in phase between the response signal and the probe signal,and to calculate the resonance frequency based on the difference inphase. The difference in phase is related to the difference between thefrequency of the probe signal and the resonance frequency of theelectrical resonator (see e.g. Halliday et al, Fundamentals of Physics,7th extended International edition. Wiley, 2005, ISBN 0-471-2321-9,pages 844-845). Resonance frequency may therefore be calculated from thephase difference. This approach may allow the use of a probe signalhaving a fixed frequency and an electrical resonator unit having a fixedtuning. This may in turn allow for the resonance frequency to bedetermined rapidly.

In some implementations, these two approaches may be combined. A firstmeasurement of resonance frequency may be performed by measuring adifference in phase between the response signal and the probe signal,the probe signal having a fixed frequency. A first estimate of theresonance frequency may be calculated based on the difference in phase.A second measurement of resonance frequency may then be performed byscanning a range of probe signal frequencies whilst measuring theamplitude and/or phase of the response signal, to obtain the secondmeasurement. The width of the range and/or a starting frequency for thescanning may be selected based on the first measurement. This may allowfor a narrower range to be scanned.

At block 202, the gate capacitance is calculated based on the resonancefrequency. The calculation may be performed by executing computerprogram code as described herein below using a processing unit. Theprocessing unit may cause the calculated resonance frequency value to bestored in working memory, written to data storage, and/or displayed to auser. Example calculations will be explained with reference to an LCcircuit.

An LC circuit has a resonance frequency which depends upon the magnitudeof the capacitance and the inductance in the circuit. The resonancefrequency may be calculated using Formula 1:

$f = \frac{1}{2\pi\sqrt{LC}}$

where f is the resonance frequency in Hz, L is the inductance in Henry(kg.m2.s-2.A-2), and C is the capacitance in Farad (s4.A2.m-2.kg-1).

As may be understood from the above formula, electrical resonator unit120 has a resonance frequency determined by the magnitudes of theinductance 122 and capacitance 124.

In the circuit 100, electrical resonator unit 120 is coupled to thesemiconductor device 140 via low impedance contact 130. Thesemiconductor device 140 has a gate capacitance. The gate capacitanceinfluences the resonance frequency of the LC circuit. The resonancefrequency of this coupled system is described by Formula 2:

$f = \frac{1}{2\pi\sqrt{L\left( {C_{res} + C_{gate}} \right)}}$

where f is the resonance frequency of the system in Hz, L is theinductance in Henry, Cres is represents the capacitance of the LCcircuit in Farad, and Cgate is the gate capacitance of the semiconductordevice in Farad.

The gate capacitance of the semiconductor device may thus be calculatedbased on the resonance frequency of the circuit 100.

Any contribution of the semiconductor device to the inductance isassumed to be 0. Current through the semiconductor component 140, andthus any contribution to the inductance of the system, is negligiblebecause semiconductor component 140 is coupled to high-impedance contact150.

The resistance and inductance of the low impedance contact 130 aredesirably as small as possible. Preferably, the resistance of the lowimpedance contact obeys the relationship:

R_(contact) ≪ 2πfC_(gate)

where Rcontact is the resistance of the low impedance contact, f is theresonance frequency of the electrical resonator, and Cgate is the gatecapacitance.

The capacitance of the low impedance contact, Ccontact, may obey therelationship:

C_(contact) > C_(gate)

This may contribute to providing a small impedance, Zcontact, since theimpedance may be described by:

$Z_{contact} = \frac{1}{2\pi ifC_{contact}}$

where i is

$\sqrt{- 1}.$

The low impedance contact may comprise a transmission line. The lowimpedance contact may include a capacitor. Alternatively, thecapacitance of the low impedance contact may be a parasitic capacitance.

Any effect of the low impedance contact on the resonance frequency ofthe system may be taken into account by calibration, as discussed below.

One technique for calibrating the circuit 100 is to perform measurementsat different applied gate voltages. The gate capacitance of asemiconductor device varies depending upon the gate voltage.

Relative gate capacitances may be determined by measuring the resonancefrequency at two or more different gate voltages.

To allow for calculation of absolute gate capacitance, a measurement maybe performed at a gate voltage selected such that the channel of thesemiconductor component is fully depleted. When the channel is fullydepleted, Cgate may be assumed to be zero.

The gate voltage which fully depletes the channel may be determinedbased on conductance measurements. Alternatively, resonance frequencymay be measured as a function of gate voltage. The maximum resonancefrequency will correspond to the minimum total capacitance, coincidingwith Cgate = 0.

In implementations where the electrical resonator unit 120 is removablyconnected to the semiconductor device 140, a still further possibilityis to calibrate the circuit by measuring the resonance frequency of theelectrical resonator unit 120 before connecting the electrical resonatorunit 120 to the semiconductor device 140. This may introduce asystematic error, because any parasitic capacitance of the connectionbetween the resonator unit 120 and semiconductor device 140 is not takeninto account.

A useful property of LC circuits is that the resonance frequency of thesystem responds linearly to changes in gate capacitance to a firstapproximation. This may be understood from a Taylor expansion of Formula2 about point C = Cres, shown below as Formula 3:

$f = \frac{1}{2\pi\sqrt{LC_{res}}} - \frac{1}{4\pi\sqrt{L}C_{res}{}^{\frac{3}{2}}} \times C_{gate}$

L and Cres are constants, therefore this formula is of the form:

f = A − B × C_(gate)

A linear response to changes in a value of interest is a desirableproperty of a measurement system.

Measuring the gate capacitance may provide insights into the performanceof the device and/or the materials used to construct the device. Forexample, measurements of gate capacitances at a plurality of differentgate voltages may allow the response of the device to changes in gatevoltage to be characterised.

Gate capacitance measurements may be used in combination withconductance measurements to investigate charge mobility, in particular,field effect mobility, in a device. This may be of particular interestfor devices for use in quantum computing, such assemiconductor-superconductor hybrid devices. The method may includemeasuring gate capacitance at a predetermined gate voltage, andmeasuring conductance at the predetermined gate voltage.

The performance of a gate dielectric may be investigated by applying avarying gate voltage and measuring gate capacitance as a function oftime. Charge trapping by the gate dielectric, for example, may cause theresponse to the gate voltage to vary.

The example of FIGS. 1 and 2 uses an LC circuit as the electricalresonator. However, other types of electrical resonator may be used. Anexample circuit 300 which uses a transmission line resonator as theelectrical resonator unit is shown in FIG. 3 .

The circuit 300 of FIG. 3 differs from circuit 100 of FIG. 1 in that theelectrical resonator unit 320 is a transmission line resonator. Thecircuit 300 further differs from circuit 100 in that high impedancecontact 150 is replaced by a switchable contact 350. In addition, FIG. 3shows further details of an illustrative IO unit 310. Circuit 300 isotherwise the same as circuit 100. The low impedance contact 330,semiconductor device and associated gate 340 are shown in simplifiedform.

The transmission line resonator 320 of this example comprises atransmission line 322 which extends between two capacitors 324 and 326.The capacitors 324, 326 may be implemented in the form of breaks in atransmission line. Each break may have a width in the range 1 µm to 100µm. An electrical signal supplied to the transmission line resonator ispartially reflected by the capacitors 324, 326. At resonance, a standingwave is formed along the transmission line 322. The length of thetransmission line 322 determine the resonance frequency of the resonator320.

The transmission line resonator may have a resonance frequency in therange 1 to 10 GHz, for example.

The switchable contact 350 of circuit 300 comprises a transistor and abias source for gating the transistor. The source of the transistor isconnected to the drain of semiconductor device 340 under investigation.The drain of the transistor is connected to ground. Gating thetransistor off (or ‘closed’) causes the transistor to act as a highimpedance contact similar to high impedance contact 150 of circuit 100,allowing for measurement of gate capacitance. Gating the transistor on(or ‘open’) allows current to flow through the transistor. This may beuseful in, for example, the measurement of conductance. Providing aswitchable contact may allow a single circuit to be used in measurementsof both gate capacitance and conductance.

A switchable contact may be paired with any type of resonator. Forexample, circuit 100 could be modified by replacing high impedancecontact 150 with a switchable contact.

Measurement of gate capacitance using circuit 300 uses the principlesexplained with reference to circuit 100. As with circuit 100, connectingthe resonator 320 to a semiconductor component 330 having a gatecapacitance causes a shift in the resonance frequency of the resonantcircuit 320 which varies depending on the applied gate voltage. One ofskill in the art will be able to adapt the equations described withreference to the LC circuit of FIG. 1 to other types of electricalresonator, such as transmission line resonator 320.

Measuring conductance comprises switching the switchable contact to alow impedance state, applying a voltage to the semiconductor device, andmeasuring current through the circuit. In examples where the electricalresonator unit is connected to the source of the semiconductor device asillustrated in FIG. 3 , the voltage may be applied through theelectrical resonator 320, since electrical resonators typically havevery little impact on conductance.

In a variant, the IO unit and electrical resonator unit may be connectedto the gate. In such a variant, switchable contact(s) may be connectedto the source and/or the drain of the semiconductor device.

IO unit 310 of this example comprises a signal generator 312, a detector314, and a circulator 316. The signal generator 312 may be, for example,a microwave generator. The signal generator 312 communicates with afirst terminal of the circulator 316. The electrical resonator unit 320communicates with a second terminal of the circulator 316. The detector314 communicates with a third terminal of the circulator 316.

Various alternative implementations of IO units are possible. The formof the IO unit is not particularly limited, provided that a probe signalcan be sent to the electrical resonator unit, and a response signal canbe received from the electrical resonator unit.

In implementations were the resonator is an LC resonator, a couplingcapacitor may be included between the IO unit and the electricalresonator unit. A coupling capacitor may be useful for combining a DCsignal with a radio-frequency excitation, or to adjust the strength ofelectrical coupling between the resonator and IO unit. Inimplementations which use a transmission line resonator, capacitor 324may act as a coupling capacitor.

In use, a probe signal from the signal generator 312 is sent to theresonator unit 320 via the circulator 316, and a response signalreceived from the resonator unit 320 is passed to the detector 314 viathe circulator 316.

An example of an apparatus 400 according to the present disclosure willnow be described with reference to FIG. 4 .

The apparatus 400 includes an IO unit 410 and a computer 420 forcontrolling the IO unit 410. The computer 420 is operably linked to anoptional user terminal 450. The apparatus 400 may be in the form of amechanical probe station, for example.

The IO unit 410 comprises a signal generator 412, a sensor 414, acirculator 416, and a connector 418.

The signal generator 412 may comprise a microwave generator. In use, thesignal generator generates a probe signal which is sent to an electricalresonator via connector 418.

The control may include activating and deactivating the signalgenerator. The control may include varying the frequency of the signalgenerated by the signal generator. The signal generator may be, forexample, a microwave generator.

IO unit 410 further includes a sensor 414. Sensor 414 is for receiving aresponse signal from a resonator. Sensor 414 may be configured tomeasure amplitude and/or phase of the response signal. Sensor 414 maycomprise, for example, a vector network analyser. Sensor 414 may beconfigured to send computer-readable data representing the responsesignal to the computer 420, for example via analogue-to-digitalconvertor circuitry.

Circulator 416 allows signal generator 412 and sensor 414 to beconnected to a single terminal of an electrical resonator via connector418. Connector 418 may take any appropriate form. For example, connector418 may comprise a needle probe, such as needle probe 500 discussedbelow with reference to FIG. 5 .

The apparatus 400 may further comprise the electrical resonator.Alternatively, the apparatus may be connectable to an externalresonator.

The computer 420 includes a processing unit 430 which is operably linkedto a data storage 440. The data storage 440 stores a computer program460 for execution by the processing unit.

The user terminal 450 may include user input equipment and a displaydevice.

The user input equipment may comprise any one or more suitable inputdevices for known in the art for receiving inputs from a user. Examplesof input devices include a pointing device, such as a mouse, stylus,touchscreen, trackpad and/or trackball. Other examples of input devicesinclude a keyboard, a microphone when used with voice recognitionalgorithm, and/or a video camera when used with a gesture recognitionalgorithm.

Where reference is made herein to receiving an input from the userthrough the user input equipment, this may mean through any one or moreuser input devices making up the user input equipment.

The user input equipment may be useful for allowing a user to initiateexecution of the computer program 460, and/or for allowing the user todefine operating parameters for the apparatus 400. For example, the userinput equipment may allow the user to input a desired frequency range tobe scanned by the signal generator 410. In implementations where theapparatus 400 is configured to control the gate voltage of thesemiconductor device, the user input equipment may allow the user tospecify one or more gate voltages. In implementations where theapparatus is connectable to an external resonator, the user inputapparatus may allow the user to input descriptors of the externalresonator such as the type of resonator, electrical parameters of theresonator, etc.

The display device may take any suitable form for outputting images,such as a light emitting diode (LED) screen, liquid crystal display(LCD), plasma screen, or cathode ray tube (CRT). The display device maycomprise a touchscreen, and thus also form at least part of the userinput equipment. A touchscreen may enable inputs by via being touched bythe user’s finger and/or using a stylus.

The inclusion of a display device is optional. A display device isuseful in implementations where it is desired to provide a graphicaloutput to a human user, such as a graph or text. As described below, thecomputer program used in the present context may generate other forms ofoutput, such as storing data in data storage 440.

The processing unit 430 may include one or more processors implementedin one or more dies, IC (integrated circuit) packages and/or housings atone or more geographic sites.

Each of the one or more processors may take any suitable form known inthe art, e.g. a general-purpose central processing unit (CPU), or adedicated form of co-processor or accelerator processor such as agraphics processing unit (GPU), digital signal processor (DSP), etc.Each of the one or more processors may comprise one or more cores.

Where it is said that a computer program is executed by the processingunit, this may mean execution by any one or more processors making upthe processing unit 430.

The processing unit 430 typically further comprises working memory, suchas random-access memory and/or one or more memory caches within the oneor more processors.

The data storage 440 comprises one or more memory units implemented inone or more memory media in one or more housings at one or moregeographic sites.

Each of the one or more memory units may employ any suitable storagemedium known in the art, e.g. a magnetic storage medium such as a harddisk drive (HDD), magnetic tape drive etc.; or an electronic storagemedium such as a solid state drive (SSD), flash memory or electricallyerasable programmable read-only memory (EEPROM), etc.; or an opticalstorage medium such as an optical disk drive or glass or memory crystalbased storage, etc.

Where it is said herein that some item of data is stored in data storage460 or a region thereof, this may mean stored in any part of any one ormore memory units making up the data storage 460.

The processing unit 430 and data storage 440 are operably linked. Theprocessing unit and data storage are configured such that processingapparatus 210 is capable of reading data from at least a portion of datastorage 440, and writing data to at least a portion of the data storage440. The processing unit 430 may communicate with the data storage 440over a local connection, e.g. a physical data bus and/or via a networksuch as a local area network or the Internet. In the latter case thenetwork connections may be wired or wireless.

The data storage 440 stores computer program code 460, i.e. software,which is executable by the processing unit 130. Executing the computerprogram code 460 may cause the apparatus 420 to perform steps of amethod of measuring a gate capacitance as provided herein.

Functionality of the computer program code 460 will be described withreference to various modules. As used herein, the term “module” is usedfor convenience of description to refer to any portion of computerprogram code configured to perform the described operation. The computerprogram code may be implemented in any appropriate manner. Theoperations of one or more modules may be combined as appropriate.

Computer program code 460 includes a control module 462 for causing theprocessing unit to control the signal generator; an identificationmodule 464 for causing the processing unit to identify, based on aninput from the sensor, a value of the resonance frequency of theelectrical resonator; a calculation module 466 for causing theprocessing unit to determine, based on the resonance frequency, a valueof the gate capacitance of the semiconductor device; and an outputgeneration module 468 for generating an output identifying the value ofthe gate capacitance.

The control module 462 may cause the processing unit 430 to activate thesignal generator and to identify the frequency of the signal generatedby the signal generator.

In implementations where the signal generator is capable of variablefrequency signal generation, the control module may cause the signalgenerator to perform a scan of a frequency range. The frequency rangemay be a range specified by a user, e.g., input via user input equipmentof the user terminal 450; a predetermined frequency range; or aprogrammatically-determined frequency range.

A predetermined frequency range may be the full dynamic range of thesignal generator.

The frequency range may be selected programmatically based on one ormore descriptors of the resonator and/or semiconductor device. Thedescriptors may include one or more of an estimated inductance of theresonator, an estimated capacitance of the resonator, and a predictedgate capacitance for the semiconductor device. The computer program codemay include a simulation module for predicting the gate capacitance ofthe semiconductor device based on e.g. the dimensions and/or materialsof the device. Limiting the range of the scan based on such descriptorsmay allow the resonance frequency to be identified more quickly.

The frequency range may be selected programmatically by calculating anestimated resonance frequency based on a difference in phase between theprobe signal and the response signal at a predetermined probe signalfrequency; and selecting a range spanning intervals on either side ofthe estimated resonance frequency. For example, a range spanning theestimated resonance frequency ± a defined tolerance may be selected.

In implementations where the electrical resonator is a tuneableelectrical resonator, such as an LC circuit including a varactor,control module 462 may cause the signal generator to operate at a fixedfrequency. Control module 462 may tune the electrical resonator, e.g. bycontrolling the output of a variable voltage source operably linked to avaractor component of the electrical resonator.

Control module 462 may record the value of the frequency. Recording maycomprise writing data to the data storage and/or holding data in theworking memory of the data processing unit, as appropriate.

The computer program code 460 further comprises an identification module464 for causing the processing unit to identify, based on an input fromthe sensor 414, a resonance frequency of the electrical resonator. Aspreviously described with reference to FIG. 1 , the strength of theresponse signal from the electrical resonator increases when thefrequency of the probe signal matches the resonance frequency of theelectrical resonator. By monitoring the response using the sensor 414,it is thus possible to identify when the electrical resonator isresonating.

Control module 462 and identification module 464 may operate inconjunction to cause the apparatus to measure the resonance frequency ofan electrical resonator-semiconductor device system, as described withreference to block 201 of FIG. 2 .

Calculation module 466 determines a gate capacitance value for thesemiconductor device based on the resonance frequency identified bymodule 464. As previously explained with reference to block 202 of FIG.2 , gate capacitance may be calculated from the resonance frequency.

Computer program code 460 may cause the apparatus to perform the methoddescribed with reference to FIG. 2 .

The computer program code 460 further includes output generation module468 for causing the processor to generating an output identifying thegate capacitance determined by module 466 is also provided.

Generating the output may comprise storing the gate capacitance value inthe data storage 440, e.g. writing the gate capacitance value to a file.Generating the output may comprise displaying the gate capacitance onthe display device of the user terminal. Generating the output maycomprise piping the output to another process, e.g. in implementationswhere further values such as a measure of charge mobility are to bedetermined based on the gate capacitance.

The apparatus 400 may further comprise one or more additionalcomponents. The computer program code 460 may include additional modulesfor controlling the operation of such components.

For example, the apparatus 400 may be configured to measure the gatevoltage which is applied to the semiconductor device. The apparatus mayinclude a voltmeter, which is configured to be connectable to a gateelectrode to measure the applied voltage e.g. via a pair of needleprobes. The computer program code may include a gate voltage monitoringmodule, for monitoring the applied voltage based on an input from thevoltmeter.

Alternatively or additionally, the apparatus 400 may be configured tocontrol the gate voltage which is applied to the semiconductor device.The apparatus may comprise a variable voltage source for applying a gatevoltage to the semiconductor device. The computer program code maycomprise a gate voltage control module, for causing the processing unitto control the variable voltage source. The computer program code may beconfigured to cause the apparatus to measure gate capacitance at two ormore different gate voltages. The computer program code may beconfigured to cause the gate voltage to vary and to monitor the responseof the gate capacitance to variations in gate voltage.

Apparatus 400 may further include a unit for measuring conductance ofthe semiconductor device. This unit may be controlled by an appropriatecomputer program code module. The computer program code module mayfurther comprise a module for determining, based on the conductancevalue and the gate capacitance value, charge mobility in the device.

One example of a unit for measuring conductance is a source measurementunit connectable to the source of the semiconductor device. In use, whenmeasuring conductance using such a unit, the drain of the semiconductordevice is connected to ground.

Another example of a unit for measuring conductance comprises currentmeter and either a voltage source or digital-to-analogue converter, DAC.The current meter is connectable to the drain of the semiconductordevice. The voltage source or DAC is connectable to the source of thesemiconductor device.

A still further example of a unit for measuring conductance comprises alock-in amplifier and a current-to-voltage converter. The lock-inamplifier has an output connectable to the source of the semiconductordevice, and an input connected to an output of the current-to-voltageconverter. The current-to-voltage converter has an input which isconnectable to the drain of the semiconductor device.

The computer program code may include a calculation module configured tocalculate charge mobility, e.g. field effect mobility, based on the gatecapacitance and conductance.

An example of a probe that may be used in combination with apparatus 400will now be explained with reference to FIG. 5 . FIG. 5 shows aschematic diagram of a resonator probe 500.

Resonator probe 500 includes a needle probe 510. A needle probe, alsoreferred to as a mechanical probe, RF probe, or probe tip, is aconductive pin or shaft that may be brought into contact with anelectrical component. In use, needle probe 510 acts as a low impedancecontact 130 as described with reference to FIG. 1 . Needle probe 510thus desirably has as low an impedance as possible. Suitable probe tipsare commercially available.

Resonator probe 500 further includes an inductor 520 and a capacitor 530connected to the needle probe 510. Resonator probe 500 thus includes anLC circuit as described with reference to electrical resonator unit 120of FIG. 1 .

In this example, capacitor 530 is a variable capacitor, morespecifically, a varactor. Varactors may also be referred to in the artas varicap diodes, variable capacitance diodes, variable reactancediodes, or tuning diodes. Varactor 530 is connected to a variable DCbias source, Vt. Although such a variable DC bias source is shown inFIG. 5 , the variable voltage source does not necessarily form part ofthe probe, and the varactor 530 may be removably connected to the DCbias source Vt by appropriate wiring or transmission lines. Varying theDC bias source voltage causes the capacitance of varactor 530 to change,thereby changing the resonance frequency of the LC circuit. The LCcircuit included in this example is thus a tuneable LC circuit.

The resonator probe 500 may be connectable to an IO unit, as previouslydescribed. In the illustrated example, the connection is via a coaxialcable 540. Coaxial cable 540 allows electrical signals to be sent to andfrom the needle probe 510. Any type of connection may be used.

In use, resonator probe 500 is used in conjunction with a passive needleprobe. The passive needle probe may comprise, or be connected to, aresistor. The passive needle probe may act as a high impedance contact150 as described with reference to FIG. 1 . The resonator probe 500 isbrought into electrical contact with one of the source, the gate, andthe drain of the semiconductor device, e.g. touched on a source terminalof the semiconductor device, or an associated transmission line e.g. PCBtrace. At the same time, the passive needle probe is brought intoelectrical contact with another terminal, which may be the source if theresonator probe connects to the drain or the gate, or may be the drainif the resonator probe connects to the source or the gate. This forms acircuit as illustrated in FIG. 1 .

The resonator probe may be configured to allow a gate voltage to beapplied via the resonator probe. Alternatively, the resonator probe maybe used in conjunction with one or more further probe(s) for applying avoltage to the gate of the semiconductor device.

It will be appreciated that the above embodiments have been described byway of example only.

More generally, according to one aspect disclosed herein, there isprovided a method of determining a gate capacitance of a semiconductordevice having a source, a drain, a gate, and a channel, thesemiconductor device being arranged in a circuit further comprising anelectrical resonator, wherein one of the source, the drain, and the gateis connected to the electrical resonator; the method comprising:measuring a resonance frequency of the circuit; and calculating, basedon the resonance frequency, the gate capacitance. Since the electricalresonator is in electrical communication with the source of thesemiconductor device, the gate capacitance of the electrical resonatorchanges the resonance frequency of the electrical resonator. The gatecapacitance may therefore be calculated based on the resonance frequencyof the system.

The source, the drain, or the gate may be connected directly to theelectrical resonator. In other words, there may be no components otherthan a connector such as a transmission line or probe between theelectrical resonator and the source, drain or gate. The electricalresonator connects to exactly one of the source, the drain, and thegate.

Measuring the resonance frequency may comprise sending a probe signalhaving a frequency to the circuit, monitoring the amplitude and/or thephase of a response signal from the circuit, and identifying theresonance frequency based on a change of the amplitude and/or phase. Adifference in phase between the response signal and the probe signal maybe measured. In some circumstances, resonance may produce a smallamplitude change but a large phase change or vice versa, thereforemonitoring both amplitude and phase may be preferred.

Measuring the resonance frequency may include varying the frequency ofthe probe signal.

Alternatively or additionally, the electrical resonator may be atuneable electrical resonator, and measuring the resonance frequency mayinclude tuning the electrical resonator.

The frequency of the probe signal and/or the tuning of the electricalresonator may be varied during the measuring. Varying both the tuning ofthe electrical resonator and the frequency of the probe signal may allowfor greater dynamic range than varying only one of the tuning and thefrequency.

Still another example step for measuring the resonance frequencycomprises may comprise sending a probe signal having a frequency to thecircuit; measuring a difference in phase between the probe signal and aresponse signal received from the circuit; and calculating the resonancefrequency based on the difference in phase. In such examples, the probesignal may have a fixed frequency and the electrical resonator may havea fixed tuning. This may allow for rapid determination of the resonancefrequency.

The probe signal may have a frequency in the range 10 MHz to 10 GHz, forexample, 1 GHz to 10 GHz. The probe signal frequency may be selected asdesired based, for example, on the nature of the electrical resonator.

In implementations where the electrical resonator is an LC resonator,the probe signal typically has a frequency in the range 10 MHz to 2 GHz.For an LC resonator, probe signal frequencies in the range 100 MHz to600 MHz, optionally 100 MHz to 500 MHz, further optionally 400 to 500MHz, may allow for improved performance in comparison with resonancefrequencies above 650 MHz.

In implementations where the resonator is a transmission line resonator,the probe signal may have a frequency in the range 1 to 10 GHz, forexample.

Varying the frequency of the probe signal may comprise performing ascan. The scan may comprise varying the frequency of the probe signal inincrements having a size in the range 0.01 and 1 MHz. The span of thescan, i.e., the width of the frequency range scanned, may be in therange 10 to 100 MHz. Calibrating the circuit may comprise scanning afrequency range with a larger span.

The nature of the semiconductor device is not particularly limited. Thesemiconductor device may, for example, comprise asemiconductor-superconductor hybrid device. Example 1 shows that thepresent method is applicable to such devices are presented herein. Otherexamples of semiconductor devices which may be investigated includefield-effect transistors, such as MOSFETs.

Typically, the semiconductor device is not a quantum dot device. Gatecapacitance is a type of ‘classical’, or geometrical, capacitance, andnot a quantum capacitance. Measuring gate capacitance typically does notcomprise measuring a readout of the state of a quantum bit.

In examples where the electrical resonator is connected to one of thesource and the drain of the semiconductor device, the other of thesource and the drain may be connected to a high impedance contact. Inexamples where the electrical resonator is connected to the gate of thesemiconductor device, one or both of the source and drain may beconnected to a respective high-impedance contact. The high-impedancecontact(s) may minimise the flow of current from the source to the drainof the semiconductor device, thereby allowing for more precisemeasurement of the gate capacitance.

A high-impedance contact may be selected from a tunnel junction; aresistor having a resistance greater than or equal to 1 MΩ, optionally10 MΩ; and a transistor, optionally a field-effect transistor, in an offstate. In implementations where the high impedance contact comprises atransistor, the method comprises gating the transistor such that thetransistor is in an off state during the measuring. The use of atransistor as the high-impedance contact may allow for easiermeasurement of the conductance of the channel of the semiconductordevice.

The method may include applying a gate voltage to the gate, andidentifying the resonance frequency of the circuit while applying thegate voltage. The method may comprise measuring two or more gatecapacitances at two or more different gate voltages.

The method may include calibrating the circuit by applying a gatevoltage selected such that the channel of the semiconductor device isnon-conductive, and identifying the resonance frequency of the circuitwhile applying the gate voltage. Gate capacitance may be assumed to bezero when the channel is non-conductive.

The gate voltage for calibrating the circuit may be identified fromconductance measurements. Alternatively, resonance frequency may bemeasured at a plurality of different gate voltages to identify a maximumresonance frequency. Gate capacitance may be assumed to be 0 when theresonance frequency is at a maximum.

The gate voltage may be varied as a function of time during theidentifying. For example, the gate voltage may be cyclically varied.Providing a gate voltage which changes with time may allow theperformance of a gate dielectric arranged between the gate and thechannel to be investigated. Charge trapping by the gate dielectric maycause the gate capacitance to vary.

The calculating may be performed by a computer comprising a processingunit operably linked to a data storage, the data storage containingcomputer program code instructions configured to cause the processor tocalculate a value of the gate capacitance based on the resonancefrequency.

The method may further comprise measuring a conductance of thesemiconductor device. In such implementations, the method may furthercomprise calculating, based on the gate capacitance and the conductance,charge mobility in the semiconductor device. The charge mobility may bea field-effect charge mobility.

Measuring conductance generally comprises applying a DC voltage acrossthe source and drain of the semiconductor device, and measuring currentthrough the channel of the semiconductor device. Electrical resonatorstypically have a low resistance, and conductance may be measured whenthe semiconductor device is in series with the electrical resonator.

In implementations where the high impedance contact is a transistor inan off state, conductance may be measured when the transistor is in anon state.

The method may further comprise performing a further measurement of gatecapacitance of the semiconductor device, wherein the further measurementis selected from a capacitance bridge measurement, a coulomb blockademeasurement, and a capacitance-voltage measurement. The furthermeasurement may be performed before measuring the gate capacitance usingthe method of the present disclosure, in order to obtain an estimate ofthe gate capacitance. This may allow for, for example, optimization ofthe range of probe signal frequencies to allow for faster measurement ofgate capacitance using the more precise method provided herein.

The electrical resonator may be removably connected to the semiconductordevice. The method may include, after identifying the resonancefrequency, disconnecting the electrical resonator from the semiconductordevice.

In implementations where the electrical resonator is removably connectedto the semiconductor device, the method may further comprise identifyingthe resonance frequency of the electrical resonator before arranging theelectrical resonator in the circuit.

The electrical resonator may be permanently connected to thesemiconductor device. For example, the electrical resonator may beintegrated onto the same chip as the semiconductor device, or connectedto the semiconductor device by wire bonding.

The nature of the electrical resonator is not particularly limited andmay be selected as appropriate. The electrical resonator may be asuperconductor resonator. More generally, the circuit may comprisesuperconductor components, normal-conductor components, or anycombination of superconductors and normal conductors.

The electrical resonator may be an LC circuit comprising an inductor anda capacitance. For an LC circuit, resonance frequency may varyapproximately linearly with gate capacitance.

The inductor may comprise a coil.

The capacitance of the LC circuit may be a parasitic capacitance.Alternatively, the capacitance may be provided by a capacitor. Thecapacitor may be a variable capacitor, such as a varactor.

The electrical resonator may be a tuneable electrical resonator. An LCcircuit which includes a variable capacitor is one example of a tuneableelectrical resonator.

Another illustrative type of electrical resonator is a transmission lineresonator. The principles explained herein are also applicable totransmission line resonators.

In another aspect, there is provided an apparatus for measuring a gatecapacitance of a semiconductor device, the semiconductor device having ahaving a source, a drain, a gate, and a channel; which apparatuscomprises: a signal generator capable of providing a probe signal to anelectrical resonator; a sensor capable of sensing the amplitude and/orphase of a response signal from the electrical resonator; a processingunit operably linked to the signal generator and the sensor; and amemory unit operably linked to the processing unit, wherein the memoryunit stores computer program code, the computer program code beingexecutable by the processing unit; wherein the computer program codecomprises: a control module for causing the processing unit to controlthe signal generator; an identification module for causing theprocessing unit to identify, based on an input from the sensor, aresonance frequency of a circuit comprising the electrical resonator; acalculation module for causing the processing unit to calculate, basedon the resonance frequency, the gate capacitance of the semiconductordevice; and an output generation module for generating an outputidentifying the gate capacitance. The apparatus may be useful forpractising the method described herein.

The circuit may comprise the electrical resonator connected to one ofthe source, the gate, and the drain of the semiconductor device.

The apparatus may further include the electrical resonator. In suchimplementations, the electrical resonator may be connectable to asemiconductor device. Alternatively, the apparatus may be removablyconnectable to the electrical resonator. For example, the apparatus maybe configured to connect to an electrical resonator which is permanentlyconnected to the semiconductor device.

The electrical resonator may be as described above with reference to themethod aspect. The electrical resonator may be a superconductorresonator.

The electrical resonator may be an LC circuit. The capacitance of the LCcircuit may be a parasitic capacitance, or may be provided by acapacitor such as a variable capacitor.

The control module and identification module may be configured to causethe apparatus to identify the resonance frequency of the electricalresonator, by sending a probe signal to the resonator using the signalgenerator, monitoring the amplitude of a response signal from theelectrical resonator using the sensor, and identifying when theamplitude is a maximum amplitude. One or more of the frequency of theprobe signal, the tuning of the electrical resonator, and the gatevoltage may be varied in order to obtain the maximum amplitude, aspreviously described with reference to the method aspect.

The calculation module may calculate the gate capacitance based on theidentified resonance frequency, e.g. using the principles explained withreference to FIG. 1 .

The output generation module may be configured to generate anyappropriate form of output. The output may comprise storing dataencoding the gate capacitance in the data storage, generating agraphical representation (e.g., text or a graph) for display to a humanuser, and/or piping the gate capacitance value to a further computerprogram.

A module may be any portion computer program code configured to causethe processing unit to perform the relevant function.

The apparatus may include a DC bias source for applying a gate voltageto the gate of the semiconductor device. The DC bias source may be avariable DC source. In implementations where the apparatus includes a DCbias source, the computer program code may further comprise a gatevoltage control module for causing the processing unit to control the DCbias source to apply a gate voltage to the gate. The computer programcode may be configured to cause the apparatus to measure gatecapacitance at two or more different gate voltages, or to vary gatevoltage during measurements, as previously described with reference tothe method aspect.

Alternatively or additionally, the apparatus may include a voltagesensor for sensing a gate voltage. The computer program code may includea voltage sensor monitoring module, for causing the processing unit toidentify a gate voltage using the voltage sensor.

In implementations where the apparatus includes, or is configured toconnect to, a tuneable electrical resonator, the apparatus may furthercomprise hardware for tuning the electrical resonator along withcomputer program code for controlling operation of that hardware. Forexample, if the tuneable electrical resonator comprises a varactor, theapparatus may include a DC bias source for applying a bias voltage tothe varactor.

The apparatus may further comprise a unit for measuring conductance ofthe semiconductor device.

One example of a unit for measuring conductance is a source measurementunit connectable to the source of the semiconductor device. In use, whenmeasuring conductance using such a unit, the drain of the semiconductordevice is connected to ground.

Another example of a unit for measuring conductance comprises currentmeter and either a voltage source or digital-to-analogue converter, DAC.The current meter is connectable to the drain of the semiconductordevice. The voltage source or DAC is connectable to the source of thesemiconductor device.

A still further example of a unit for measuring conductance comprises alock-in amplifier and a current-to-voltage converter. The lock-inamplifier has an output connectable to the source of the semiconductordevice, and an input connected to an output of the current-to-voltageconverter. The current-to-voltage converter has an input which isconnectable to the drain of the semiconductor device.

The unit for measuring conductance unit may be controlled by anappropriate computer program code module. The computer program code mayfurther comprise a module for determining, based on the conductancevalue and the gate capacitance value, charge mobility in the device.

The apparatus may comprise a mechanical probe station, furthercomprising first and second needle probes. The first needle probe may bea resonator probe, and the second needle probe may be a passive needleprobe. Alternatively, both the first needle probe and the second needleprobe may be passive needle probes.

A related aspect provides a probe for measuring a gate capacitance. Theprobe is configured to be connectable to an apparatus, such as theapparatus as described with reference to the previous aspect, to receivea probe signal from the apparatus and to provide a response signal fromthe LC circuit to the apparatus.

The probe may comprise a needle probe, an inductor, and a capacitor. Theneedle probe, inductor, and capacitor are configured as an LC circuit. Aprobe comprising an LC circuit is referred to herein as a resonatorprobe.

The capacitor may be a varactor. In implementations where a varactor isused, the LC circuit is tuneable by applying a DC bias to the varactorthereby varying its capacitance and hence, the resonance frequency ofthe LC circuit.

The resonator probe may be used in combination with a high-impedanceprobe. The high-impedance probe may comprise a needle probe and aresistor having a resistance of greater than or equal to 1 MΩ, e.g.greater than or equal to 10 MΩ.

Alternatively, the resonator probe may be used in combination with avariable-impedance probe comprising a needle probe and a transistor. Inuse, the transistor is gated to an “off” state during measurement ofgate capacitance. The variable impedance probe may also be used tomeasure conductance, by gating the transistor to an “on” state.

A further related aspect provides a use of the above-described probe inthe measurement of a gate capacitance of a semiconductor device, thesemiconductor device having a having a source, a drain, a gate, and achannel.

Another aspect provides a computer program product comprising computerprogram code which, when executed by a processor, causes the processorto: process an input to identify a resonance frequency of a circuitcomprising an electrical resonator; calculate, based on the resonancefrequency, a gate capacitance; and generate an output identifying thegate capacitance. The computer program product may be embodied on anon-transitory computer readable medium. A related aspect provides acomputer readable storage medium having stored thereon the computerprogram product.

The circuit may comprise the electrical resonator connected to one ofthe source, the gate, and the drain of the semiconductor device.

The input may be received from a sensor, read from a data storage,received over a network, received from another computer program, orentered by a user.

Calculating the gate capacitance from the resonance frequency maycomprise applying the principles described hereinabove.

The output may comprise storing data encoding the gate capacitance inthe data storage, generating a graphical representation (e.g., text or agraph) for display to a human user, and/or piping the gate capacitancevalue to a further computer program.

The computer program may comprise the computer program code describedwith reference to the apparatus aspect.

Example 1

In order to demonstrate that the gate capacitance of a semiconductorhybrid device may be measured using the method of the presentdisclosure, measurements were performed on an illustrative device. Ascanning electron microscopy, SEM, micrograph of the device is shown inFIG. 6 .

The illustrative device includes a nanowire 601 of semiconductormaterial which is gated by a set of finger gates 602 a to 602 e. Gatecapacitance is formed in the region 603 when an electrostatic field isapplied to the nanowire 601 using one or more of the finger gates 602 ato 602 e. The area of the nanowire 601 which was in contact with each ofthe finger gates 602 a to 602 e had dimensions of approximately 80 nm ×100 nm.

In order to measure the gate capacitance, a contact pad of the devicewas connected to an LC resonator. The resonance frequency of the LCresonator was measured with a varying number of active finger gates. Theresults of this investigation are shown in a FIG. 7 .

As may be seen from FIG. 7 , changes in gate capacitance as a result ofopening the finger gates were detected as changes in the resonancefrequency of the LC circuit. As is shown in FIG. 7 , changes in thecapacitance were of the order of 10 attofarads, and differences of thissize were easily measurable. The inventors believe that a sensitivity of1 attofarad is achievable using the present method.

Example 2

Simulations were performed to estimate the accuracy of the methodprovided herein. The simulated system is illustrated in FIG. 8 .Capacitance, resistance and inductance values used for the simulationwere based on the test device discussed in Example 1 and are thusbelieved to reflect real-world conditions.

Capacitance values were calculated on the basis of resonance frequency,and plotted against the true gate capacitance of the simulated system.The result of this are shown in FIG. 9 .

As may be seen from the figure, very good agreement between thereconstructed capacitance and the true capacitance was obtained.Systematic errors were estimated to be less than 1%.

A corresponding plot of relative error between the reconstructed andtrue values against the true capacitance is provided in FIG. 10 . Forvalues in the femtofarad range or smaller, relative errors were verysmall. Gate capacitances in the devices of interest generally fallwithin this range.

Other variants or use cases of the disclosed techniques may becomeapparent to the person skilled in the art once given the disclosureherein. The scope of the disclosure is not limited by the describedembodiments but only by the accompanying claims.

1-15. (canceled)
 16. A method of determining a gate capacitance of asemiconductor device having a source, a drain, a gate, and a channel,the semiconductor device being arranged in a circuit further comprisingan electrical resonator, wherein one of the source and the drain isconnected to the electrical resonator, and the other of the source andthe drain is connected to a high-impedance contact, the high-impedancecontact being selected from a tunnel junction, a resistor having aresistance greater than or equal to 1 MQ, and a transistor in an offstate; the method comprising: measuring a resonance frequency of thecircuit; and calculating, based on the resonance frequency, the gatecapacitance.
 17. The method according to claim 16, wherein measuring theresonance frequency comprises sending a probe signal having a frequencyto the circuit, monitoring at least one parameter selected from theamplitude and phase of a response signal from the circuit, andidentifying a change of the at least one parameter.
 18. The methodaccording to claim 17, wherein measuring the resonance frequencyincludes varying the frequency of the probe signal to cause the change.19. The method according to claim 17, wherein the electrical resonatoris tuneable, and wherein measuring the resonance frequency includestuning the electrical resonator.
 20. The method according to claim 17,wherein the probe signal has a frequency in the range 10 MHz to 10 GHz.21. The method according to claim 16, including applying a gate voltageto the gate, and measuring the resonance frequency of the circuit whileapplying the gate voltage.
 22. The method according to claim 21, whereinthe method comprises determining a gate capacitance at two or moredifferent gate voltages.
 23. The method according to claim 21, furthercomprising varying the gate voltage during the measuring.
 24. The methodaccording to claim 16, further comprising measuring a conductance of thesemiconductor device.
 25. The method according to claim 16, furthercomprising performing an additional measurement of gate capacitance ofthe semiconductor device, wherein the additional measurement is selectedfrom a capacitance bridge measurement, a coulomb blockade measurement,and a capacitance-voltage measurement.
 26. The method according to claim16, wherein the electrical resonator is an LC circuit comprising aninductor and a capacitance; and the capacitance is a parasiticcapacitance, or wherein the capacitance is provided by a varactor. 27.The method according to claim 16, wherein the electrical resonator is atransmission line resonator.
 28. The method according to claim 16,wherein the electrical resonator is connected to the gate.
 29. Themethod according to claim 16, wherein measuring the resonance frequencycomprises sending a probe signal having a frequency to the circuit;measuring a phase difference between the probe signal and a responsesignal received from the circuit; and calculating the resonancefrequency based on the phase difference.
 30. An apparatus fordetermining a gate capacitance of a semiconductor device, thesemiconductor device having a having a source, a drain, a gate, and achannel; the apparatus comprising: an electrical resonator connected toone of the source and the drain of the semiconductor device; a highimpedance contact connected to the other of the source and the drain ofthe semiconductor device; a signal generator capable of providing aprobe signal to the electrical resonator; a sensor capable of sensing atleast one of amplitude and phase of a response signal from theelectrical resonator; a processing unit operably linked to the signalgenerator and the sensor; and a memory unit operably linked to theprocessing unit, wherein the memory unit stores computer program code,the computer program code being executable by the processing unit;wherein the computer program code comprises: a control module configuredto cause the processing unit to control the signal generator; anidentification module configured to cause the processing unit toidentify, based on an input from the sensor, a resonance frequency ofthe electrical resonator; a calculation module configured to cause theprocessing unit to calculate, based on the resonance frequency, the gatecapacitance of the semiconductor device; and an output generation moduleconfigured to generate an output identifying the gate capacitance. 31.The apparatus according to claim 30, wherein the electrical resonator isan LC circuit comprising an inductor and a capacitance.
 32. Theapparatus according to claim 30, wherein the LC circuit includes avaractor.
 33. The apparatus according to claim 30, further comprising afirst probe configured to be connected to the source of thesemiconductor device, and a second probe configured to be connected tothe drain of the semiconductor device.
 34. The apparatus according toclaim 30, further comprising a unit for measuring conductance of thesemiconductor device.
 35. A computer program product embodied on anon-transitory computer readable medium, comprising computer programcode which, when executed by a processor, causes the processor to:process an input to identify a resonance frequency of a circuitcomprising an electrical resonator; calculate, based on the resonancefrequency, a gate capacitance; and generate an output identifying thegate capacitance.